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Spring question

  1. May 23, 2005 #1
    one more spring question :smile:

    A block collides with a spring on a horizontal surface

    the block compresses the spring x metres from rest position. What was its speed at the instant of collision

    Ok so far I know how to do this question

    Ee = Ek
    .5kx^2 = .5mv^2

    but in this question there is a coefficient of kinetic friction between the block and the surface.. not sure how it fits in.

    I'm thinking that it is only affecting the Ee part of the equation..so:

    Ee = Ek
    .5ukx^2 = .5mv^2

    is this right?
  2. jcsd
  3. May 23, 2005 #2


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    Homework Helper

    Well, you can still use conservation of energy, only you have to take into account the work done against friction as well. The friction is a constant force, so things are kept simple.

    Do you know [tex]F_{fr} = \mu N[/tex], to relate the frictional force to the normal force of the surface on the block ? N, is of course, equal to the weight of the block considering that this is a horizontal surface.

    The work done against friction is [tex](F_{fr})(x)[/tex], since x is the distance moved in the direction of the force.

    Then just use conservation of energy :

    Initial energy of system = Final energy of system

    Initial KE of block = Work done against friction (dissipated as heat to surface and block) + Potential Energy stored in spring.

    [tex]\frac{1}{2}mv^2 = \mu mgx + \frac{1}{2}kx^2[/tex]

    and express v in terms of [itex]\mu[/itex], m, g, k and x.
    Last edited: May 23, 2005
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